Trails
Trails Follow Water 
Water was an important necessity to migrating animals and travelers on land so it is not surprising that the Native American trails followed the bison on the plains. Both hugged Nebraska's greatest of rivers, the Platte River. The early settlers used these same trails and paths as the roads to the great west.
Our modern roads follow in the footsteps of our ancestors and stray very little as the early roads were improved. New projects such as the Interstate Highway system also tend to follow the same general paths in order to supplement the commerce of the already established cities. As Interstate 80 makes its way across Nebraska, it too hugs the Platte River for much of the way.
Lewis & Clark National Historic Trail 
The Lewis & Clark National Historic Trail is along the route that the Corp of Discovery Expedition traveled on their way to the west coast. It travels along the Missouri River, and on beyond the nebraska State borders on to the west coast. It marks important placea long the way.
The National Park Service has the best map I have seen developed to show the Lewis & Clark National Historic Trail Trail, and including a lot of the historic locations along the way:
Lewis & Clark National Historic Trail Map
Mormon Trail 
When the Mormons left "Winter Quarters" and the Kanesville area (Council Bluffs), they headed straight for the Platte River around Fremont and stuck with it throughout most of the state and on into Wyoming. The only deviation being between Columbus and Grand Island. At Columbus, the (collective) Loup Rivers feeds the Platte River from the North. Since the Mormons were traveling on the northern edge they continued on with the North Loup River on its North side until finally a decision was made to travel south and join back in with the Platte River around Grand Island. As some of the first needing to get covered wagons through narrow passes, the Mormons contributed to improving the road's conditions and width.
The National Park Service has the best map I have seen developed to show the Mormon Trail, and including a lot of the historic locations along the way:
Mormon Pioneer National Historic Trail Map
The Mormon Trail was later referred to as the California Trail when gold seekers crossed Nebraska to the rivers and valleys of California around Sacramento.
Sidney-Deadwood Trail 
The Sidney-Deadwood Trail was used to herd cattle from Deadwood, South Dakota, south to the cattle sales in Texas. It passes through Crawford in northwest Nebraska and continues south through Sidney and Bridgeport where it follows the same path as the Oregon Trail before leaving the state as it travels on south.
Oregon National Historic Trail 
The Oregon Trail started south of the Nebraska territory, back in Missouri, but as the travelers made their way west, they crossed into Nebraska and continued along the southern edge of the Platte River around Kearney. Before joining up with the Platte River, the Oregon Trail used another river, the Little Blue River right up to the point that offered the shortest jump over to the Platte.
At Fort Sidney, the southern branch of the Oregon Trail turned north to join up with the northern branch around Bridgeport, Nebraska, continuing on towards Scottsbluff. Between Sidney and Bridgeport, the Oregon trail follows a similar path as the Sidney Deadwood Trail, which continues on north into South Dakota.
Idaho University Website on the Oregon Trail
The National Park Service has the best map I have seen developed to show the Oregon Trail, and including a lot of the historic locations along the way:
Oregon National Historic Trail Map
Pony Express 
To supply these early settlers with news from back east and to report on the riches found in the west to the folks back east, the Pony Express was formed to get mail from St. Joseph, Missouri to Sacramento, California. It took the same general route of the Oregon Trail.* Though the Pony Express only existed for less than 2 years (April 3, 1860-October 1861*), it has remained an important part of the development of the West and Nebraska's history.
Oxbow Trail 
The Oxbow Trail that starts around Nebraska City meanders through Nebraska up to near Columbus where it hugged close to the Platte River to its end around Grand Island.
Nebraska City Cut-off Trail 
The Nebraska City Cut-off Trail is the shortest route to Grand Island from Nebraska City. There it joins in with the Oregon Trail to the west.